摘要
讨论了有源函数的热传导方程ｕｔ—△ｕ＋ｑ（Ｘ）ｕ＝ｆ（Ｘ，ｔ）ｕ（Ｘ，０）＝ｇ（Ｘ）其中ｑ（Ｘ）为未知函数，在附加条件ｕ（ｘ，Ｔ）＝ｈ（ｘ）下反问题（ｕ，ｑ）的存在性。用Ｇａｌｅｒｋｉｎ逼近法和拓扑度理论得出了反问题的存在性定理。
In this paper, the existence of the inverse problem for the following heat conduction problem with a source function under the condition of u(x, T)= h (x) is studied, where q (x) is an unknown function. An ekistence theorem of inverse problem is given by the Galerkin approximation method and the theory of toplogical degree.
关键词
反问题
热传导方程
有源函数
Inverse Problem
Extremum Principle
Galerkin Approximation
Topological Degree
sSobolev Embeding
